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Abstract:

An analysis method for turbine-generator torsional vibrations affected by
power transmission system, which is processed by a computer system with a
simulation software, is proposed. This analysis method comprises:
building structures of a first system model and a second system model to
respectively simulate a first system and a second system; building
detailed models of the first and second system model; and analyzing the
detailed models of the first and second system model in frequency- and
time-domain.

Claims:

1. An analysis method for turbine-generator torsional vibrations affected
by power transmission system, which is processed by a computer system
with a simulation software, comprising: building structures of a first
system model and a second system model to respectively simulate a first
system and a second system; building detailed models of the first and
second system model; and analyzing the detailed models of the first and
second system model in frequency- and time-domain.

2. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 1, wherein the
first system model has a three-phase transmission module.

3. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 1, wherein the
first system model comprises a turbine-generator, a first power
transmission system, and a power network, the turbine-generator has a
turbine and a generator driven by the turbine, the first power
transmission system has a first transformer, a three-phase transmission
module, and a second transformer connected in series, and the power
network is an infinite bus system.

4. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 3, wherein the
first transformer is a Delta-Wye-Ground transformer, the three-phase
transmission module is a single-circuit three-phase line system, and the
second transformer is a Wye-Ground-Delta transformer.

5. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 1, wherein
second system model has a four-phase transmission module.

6. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 5, wherein the
second system model comprises a turbine-generator, a second power
transmission system, and a power network, the turbine-generator has a
turbine and a generator driven by the turbine, the second power
transmission system has a third transformer, a four-phase transmission
module, and a fourth transformer connected in series, and the power
network is an infinite bus system.

7. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 6, wherein the
third transformer is a Scott-+-Ground transformer, the four-phase
transmission module is a single-circuit four-phase line system, the
second transformer is a +-Ground-Scott transformer.

8. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 7, wherein the
third transformer has a first input port, a second input port, a third
input port, a first transforming unit, a second transforming unit, a
third transforming unit, a first output port, a second output port, a
third output port, a fourth output port, and a ground end, each of the
first transforming unit, second transforming unit and third transforming
unit has a primary side providing an "s" input end and a "t" input end
and a secondary side providing a "w" output end, an "x" output end, a "y"
output end and a "z" output end, the "s" input end of the first
transforming unit serves as the first input port, the "t" input ends of
the first transforming unit and second transforming unit and the "s"
input end of the third transforming unit are connected, the "s" input end
of the second transforming unit serves as the second input port; the "t"
input end of the third transforming unit serves as the third input port,
the "w" output end of the first transforming unit serves as the first
output port, the "x" and "y" output ends of the first transforming unit
connect with the ground end, the "z" output ends of the first
transforming unit serves as the third output port, the "w" output end of
the second transforming unit serves as the second output port, the "x"
output end of the second transforming unit connects with the "w" output
end of the third transforming unit, the "y" output end of the second
transforming unit connects with the ground end, the "z" output end of the
second transforming unit connects with the "y" output end of the third
transforming unit, the "x" output end of the third transforming unit
connects with the ground end, and the "z" output end of the third
transforming unit serves as the fourth output port.

9. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 1, wherein the
detailed models of each of the first and second system models comprise a
turbine-generator mechanistic model, a fan wheel mechanistic model, a
turbine-generator electric model, and a transformer model.

10. The analysis method for turbine-generator torsional vibrations
affected by power transmission system as claimed in claim 9, wherein the
turbine-generator mechanistic model comprises models of a turbine set and
a generator, the turbine set is represented by a high pressure turbine, a
front part of a first stage low pressure turbine, a rear part of the
first stage low pressure turbine, a front part of a second stage low
pressure turbine and a rear part of the second stage low pressure
turbine, each of the front and rear parts of the first and second stage
low pressure turbines has a fan wheel set with 11 stages, and the
generator including a generator rotor, a commutator rotor, and an
exciting rotor.

Description:

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to an analysis method for
turbine-generator torsional vibrations and, more particularly, to an
analysis method for turbine-generator torsional vibrations due to power
transmission system.

[0003] 2. Description of the Related Art

[0004] Presently, the power transmission structure of Taiwan is mainly
distributed at the west coast of Taiwan like a narrow belt, which is
briefly divided into "North part," "Center part" and "South part"
connected by transmission lines with a high voltage level of 345 kV, and
a sketch of the pylon, arrangement of conductors and voltage-time diagram
of the used three-phase power transmission system are shown in FIGS. 1a,
1b and 1c. Owing to the increasing population of the west coast, it is
hard to obtain sufficient and suitable lands for pylons and substations
for any new transmission line. On the other hand, power transmission for
transmitting electrical power from the "South part" and "Center part" to
the "North part" is truly important for the Taiwan power transmission
structure since the population of the north part in Taiwan is much higher
than those of the other parts. However, the above fact results in a high
loading of the power transmission lines, a large rotor angle difference
between north and south parts of Taiwan power plants, and worse stability
of power supply. Therefore, how to increase the capacity of a power
transmission system has become an important issue in this field.

[0005] Please refer to FIGS. 2a, 2b and 2c, which are a sketch of the
pylons, arrangement of conductors and voltage-time diagram of a
four-phase power transmission system. Adjusting the used three-phase
power transmission system to a four-phase power transmission system may
actually improve the capacity of power transmission lines because a
four-phase power transmission system has properties such as high
transient stability, low interference induced by electromagnetic filed,
and reduced conductor arrangement in space. Besides, the four-phase power
transmission system is a power transmission system with even number of
phases and similar to the conventional three-phase power transmission
system. Therefore, the four-phase power transmission system may be an
acceptable solution for the situation in Taiwan.

[0006] However, most of the studies of a four-phase power transmission
system are focused on transformation technique, differential protection
from a three-phase power transmission system to a four-phase power
transmission system, and economic analysis, and none of them is about
interaction effects on connected turbine-generator and four-phase power
transmission system.

[0007] Moreover, in order to acquire a low cost in power generation and
high thermal efficiency, the scales of power generators are gradually
increased because nuclear power generations were introduced to Taiwan.
However, once the scales of power generators are increased, transient
fault accident of the power transmission system can easily result in
torsional vibrations of fan wheel and rotor shaft of the
turbine-generator and lead to fatigue life expenditure problems on the
fan wheel and rotor shaft.

[0008] Accordingly, it is necessary to analyze the affection of torsional
vibrations to the turbine-generator caused by transient fault of the
power transmission system prior to actually applying the four-phase power
transmission system to the power transmission structure of Taiwan. Thus,
an analysis method for turbine-generator torsional vibrations affected by
power transmission system is required to examine the feasibility and
effectiveness of a four-phase power transmission system.

SUMMARY OF THE INVENTION

[0009] It is therefore the primary objective of this invention to provide
an analysis method for turbine-generator torsional vibrations affected by
power transmission system, by which models and analyses are made for
ensuring the feasibility and effectiveness of a four-phase power
transmission system.

[0010] The invention discloses an analysis method for turbine-generator
torsional vibrations affected by power transmission system, which is
processed by a computer system with a simulation software, comprises:
building structures of a first system model and a second system model to
respectively simulate a first system and a second system; building
detailed models of the first and second system model; and analyzing the
detailed models of the first and second system model in frequency- and
time-domain.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The present invention will become more fully understood from the
detailed description given hereinafter and the accompanying drawings
which are given by way of illustration only, and thus are not limitative
of the present invention, and wherein:

[0012] FIG. 1a shows a sketch diagram of a pylon of a conventional
three-phase power transmission system.

[0013] FIG. 1b shows a sketch diagram of an arrangement of conductors of a
conventional three-phase power transmission system.

[0015]FIG. 2a shows a sketch diagram of a pylon of a conventional
four-phase power transmission system.

[0016] FIG. 2b shows a sketch diagram of an arrangement of conductors of a
conventional four-phase power transmission system.

[0017]FIG. 2c shows a voltage-time diagram of a conventional four-phase
power transmission system.

[0018] FIG. 2d shows the transformer diagram of a three-phase to
four-phase conversion.

[0019] FIG. 3 shows a block diagram of an analysis method of a preferred
embodiment of the invention.

[0020]FIG. 4a shows a structure of a first system model of the analysis
method of the preferred embodiment of the invention.

[0021]FIG. 4b shows a structure of a second system model of the analysis
method of the preferred embodiment of the invention.

[0022]FIG. 5 shows a structure of a turbine-generator mechanistic model
of the analysis method of the preferred embodiment of the invention.

[0023]FIG. 6 shows a structure of a fan wheel mechanistic model of the
analysis method of the preferred embodiment of the invention.

[0024]FIG. 7 shows a structure of a turbine-generator electric model of
the analysis method of the preferred embodiment of the invention.

[0025] FIG. 8 shows a structure of a Scott-Four-phase model of the
analysis method of the preferred embodiment of the invention.

[0026] In the various figures of the drawings, the same numerals designate
the same or similar parts. Furthermore, when the term "first," "second,"
"third", "fourth" and similar terms are used hereinafter, it should be
understood that these terms refer only to the structure shown in the
drawings as it would appear to a person viewing the drawings, and are
utilized only to facilitate describing the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0027] Referring to FIG. 3, a block diagram illustrating a preferable
embodiment of the present invention of an analysis method for
turbine-generator torsional vibrations affected by power transmission
system is shown, wherein the analysis method includes a structure
building step S1, a model building step S2, and an analyzing step S3.

[0028] In the structure building step S1, structures of a first system
model and a second system model are built to respectively simulate a
first system and a second system. In this embodiment, the first system
model simulates a combination of a three-phase power transmission system
and a turbine-generator, and the second system model simulates a
combination of a four-phase power transmission system and a
turbine-generator.

[0029] In detail, referring to FIG. 4a, the structure of the first system
model includes a turbine-generator 1, a first power transmission system
2, and a power network 3. The turbine-generator 1 includes a turbine set
11 and a generator 12 driven by the turbine set 11; the first power
transmission system 2 includes a first transformer 21, a three-phase
transmission module 22, and a second transformer 23; and the power
network 3 is an infinite bus system. In this embodiment, there is a
plurality of turbines 111 in the turbine set 11 with each turbine 111
having a plurality of blades. The generator 12 includes a generator rotor
121, a commutator rotor 122, and an exciting rotor 123 in serial
connection, with the generator rotor 121 connecting with the turbines 111
of the turbine set 11. The first transformer 21 is a Delta-Wye-Ground
transformer with the capacity of 1057 MVA. The three-phase transmission
module 22 is a single-circuit three-phase line system with a high voltage
level of 345 kV, which includes power transmission lines "A," "B," "C"
and two circuit breaks "CB." The second transformer 23 is a
Wye-Ground-Delta transformer.

[0030] Referring to FIG. 4b, the difference between the structures of the
first and second system models lies in that, in the second system model,
the first power transmission system 2 in the first system model is
substituted by a second power transmission system 4. The second power
transmission system 4 includes a third transformer 41, a four-phase
transmission module 42, and a fourth transformer 43, which are connected
in series. The third transformer 41 is a Scott-+-Ground transformer with
the capacity of 1057 MVA. The four-phase transmission module 22 is a
single-circuit four-phase line system with a high voltage level of 211.3
kV, which includes power transmission lines "a," "b," "c," "d" and two
circuit breaks "CB." The second transformer 23 is a +-Ground-Scott
transformer.

[0031] In the second model building step S2, details of the first and
second system models are built, wherein a turbine-generator mechanistic
model, a fan wheel mechanistic model, a turbine-generator electric model,
and a transformer model are introduced.

[0032] Referring to FIG. 5, the turbine-generator mechanistic model is
presented in a mass-damping-spring form, which includes models of the
turbine set 11 and generator 12. Specifically, the plural turbines 111 of
the turbine set 11 are represented by a high pressure turbine "HP," a
front part of a first stage low pressure turbine "LP1F," a rear part of
the first stage low pressure turbine "LP1R," a front part of a second
stage low pressure turbine "LP2F," and a rear part of the second stage
low pressure turbine "LP2R," with each of the front and rear parts of the
first and second stage low pressure turbines "LP1F," "LP2F," "LP1R" and
"LP2R" having a respective fan wheel set "B1F," "B2F," "B1R" or "B2R."
Each of the fan wheel sets "B1F," "B2F," "B1R," "B2R" has 11 stages,
while the prior 9 stages of each fan wheel set "B1F," "B2F," "B1R" or
"B2R" are connected in series by tubular air channel.

[0033] In the models of the turbine set 11 and generator 12, mass elements
"Ih," "I.sub.LP1F," "I.sub.LP1R," "I.sub.LP2F," "I.sub.LP2R,"
"Ig," "Ir" and "Ie" respectively represent the inertia
factors of the high pressure turbine "HP," front part of the first stage
low pressure turbine "LP1F," rear part of the first stage low pressure
turbine "LP1R," front part of the second stage low pressure turbine
"LP2F," rear part of the second stage low pressure turbine "LP2R,"
generator rotor 121, commutator rotor 122, and exciting rotor 123. Spring
elements "Kh1," "K1fr," "K12," "K2fr," "K2g,"
"Kgr," and "Kre" respectively represent the rigidity factors
between the high pressure turbine "HP" and the front part of the first
stage low pressure turbine "LP1F," the front part of the first stage low
pressure turbine "LP1F" and the rear part of the first stage low pressure
turbine "LP1R," the rear part of the first stage low pressure turbine
"LP1R" and the front part of the second stage low pressure turbine
"LP2F," the front part of the second stage low pressure turbine "LP2F"
and rear part of the second stage low pressure turbine "LP2R," the rear
part of the second stage low pressure turbine "LP2R" and the generator
rotor 121, the generator rotor 121 and the commutator rotor 122, and the
commutator rotor 122 and exciting rotor 123. Damper elements "Dh,"
"D1f," "D1r," "D2f," "D2r," "Dg," "Dr" and
"De" respectively represent the damping factors of the high pressure
turbine "HP," front part of the first stage low pressure turbine "LP1F,"
rear part of the first stage low pressure turbine "LP1R," front part of
the second stage low pressure turbine "LP2F," rear part of the second
stage low pressure turbine "LP2R," generator rotor 121, commutator rotor
122, and exciting rotor 123. Moreover, Damper elements "Dh1,"
"D1fr," "D12," "D2fr," "D2g," "Dgr," and
"Dre" respectively represent the damping factors between the high
pressure turbine "HP" and the front part of the first stage low pressure
turbine "LP1F," the front part of the first stage low pressure turbine
"LP1F" and the rear part of the first stage low pressure turbine "LP1R,"
the rear part of the first stage low pressure turbine "LP1R" and the
front part of the second stage low pressure turbine "LP2F," the front
part of the second stage low pressure turbine "LP2F" and the rear part of
the second stage low pressure turbine "LP2R," the rear part of the second
stage low pressure turbine "LP2R" and the generator rotor 121, the
generator rotor 121 and the commutator rotor 122, and the commutator
rotor 122 and exciting rotor 123.

[0034] Referring to FIG. 6, the fan wheel mechanistic model is also
presented in a mass-damping-spring form. For convenient illustration,
only the mechanistic model of one stage of the fan wheel with 11 stages
in the rear part of the first stage low pressure turbine "LP1R" is shown.
In detail, for example, in addition to the mass element "I.sub.LP1R," the
spring elements "K1fr," "K12," and the Damper elements
"D1r," "D1fr," "D12" shown in FIG. 6, a flexibility
element "Jbf" representing the flexibility factor of the single
stage of the fan wheel, a flexural spring element "Kbf" representing
the flexural rigidity factor thereof, and a flexural damper element
"Dbf" representing the flexural damping factor thereof are used.
There are three kinds of vibration modes of a fan wheel since the fan
wheel is a flexible device and can be affected by flexural deformation,
cold shrink, and dynamic coupling effect. The said three modes are
flexural mode, axial mode and torsional mode, wherein the flexural mode
occurs in radial directions of the fan wheel with low frequency and large
vibration, the axial mod occurs in axial directions of the fan wheel, and
the torsional mode occurs in peripheral direction of the fan wheel.
Besides, torsion of the fan wheel can be represented by torsion equation
as the following:

[0035] In the above equations, φj and ωj respectively
represent the angular displacement and angular velocity of a rotor inside
a j-th stage fan wheel while the φBj and ωBj
respectively represent the angular displacement and angular velocity of
the j-th stage fan wheel.

[0036] Referring to FIG. 7, the inertia-damping-stiffness coefficients for
turbine-generator mechanical model is transformed to an
inductance-resistance-capacitance network through electromechanical
analogy theory. For convenient illustration, only the turbine-generator
electric models of the rear part of the second stage low pressure turbine
"LP2R" and the generator rotor 121 are shown. In the FIG. 7, capacitances
"1/K2FR," "1/K2G," and "1/KGR" respectively represent the
rigidity factors between the front part of the second stage low pressure
turbine "LP2F" and rear part of the second stage low pressure turbine
"LP2R," the rear part of the second stage low pressure turbine "LP2R" and
the generator rotor 121, and the generator rotor 121 and the commutator
rotor 122. Resistances "D2FR," "D2G," and "DGR"
respectively represent the damping factors between the front part of the
second stage low pressure turbine "LP2F" and the rear part of the second
stage low pressure turbine "LP2R," the rear part of the second stage low
pressure turbine "LP2R" and the generator rotor 121, and the generator
rotor 121 and the commutator rotor 122. A capacitance "K.sub.B2R," an
inductance "I.sub.B2R" and a resistance "D.sub.B2R" respectively
represent the rigidity factor, inertia factor and damping factor of the
fan wheel "B2R" of the rear part of the second stage low pressure turbine
"LP2R." Resistances "DG" and "D2R" respectively represent
damping factors of the generator rotor 121 and the rear part of the
second stage low pressure turbine "LP2R." Inductances "IG" and
"I.sub.LP2R" respectively represent the inertia factors of the generator
rotor 121 and the rear part of the second stage low pressure turbine
"LP2R." A voltage source "TE/m" represents an E/M torque of a rotor.

[0037] In this embodiment, a computer system with a simulation software,
such as a Matlab-Sim-Power-System, previously installed therein is used
to build these models. Specifically, a synchronous machine model of
"Fundamental Parameters in propulsion unit" is used to simulate
generators of the turbine set 11, a DYg Tri-phase model is used to
simulate the first transformer 21 and second transformer 23, a R-L
Tri-phase model is used to simulate the three-phase transmission module
22, and a R-L equivalent voltage source model is used to simulate the
power network 3.

[0038] Referring to FIG. 8, a sketch diagram of a Scott-Four-phase model
representing the third transformer 41 is shown, with the Scott-Four-phase
model has a first input port 41A, a second input port 41B, a third input
port 41C, a first transforming unit 411, a second transforming unit 412,
a third transforming unit 413, a first output port 41a, a second output
port 41b, a third output port 41c, a fourth output port 41d, and a ground
end 41n. Each of the first transforming unit 411, second transforming
unit 412 and third transforming unit 413 has a primary side providing an
"s" input end and a "t" input end and a secondary side providing a "w"
output end, an "x" output end, a "y" output end and a "z" output end.
Specifically, the "s" input end of the first transforming unit 411 serves
as the first input port 41A, the "t" input ends of the first transforming
unit 411 and second transforming unit 412 and the "s" input end of the
third transforming unit 413 are connected; the "s" input end of the
second transforming unit 412 serves as the second input port 41B; the "t"
input end of the third transforming unit 413 serves as the third input
port 41C. Moreover, the "w" output end of the first transforming unit 411
serves as the first output port 41a; the "x" and "y" output ends of the
first transforming unit 411 connect with the ground end 41n; the "z"
output ends of the first transforming unit 411 serves as the third output
port 41c; the "w" output end of the second transforming unit 412 serves
as the second output port 41b; the "x" output end of the second
transforming unit 412 connects with the "w" output end of the third
transforming unit 413; the "y" output end of the second transforming unit
412 connects with the ground end 41n; the "z" output end of the second
transforming unit 412 connects with the "y" output end of the third
transforming unit 413; the "x" output end of the third transforming unit
413 connects with the ground end 41n; and the "z" output end of the third
transforming unit 413 serves as the fourth output port 41d.

[0039] In the analyzing step S3, the first and second system models are
analyzed in frequency- and time-domain. Specifically, in frequency
domain, when a disturbance occurs in the power transmission system, the
disturbance will transfer into an E/M torque comprising an unidirectional
component, a system-frequency component, and a double system-frequency
component. Therefore, analyses of unidirectional components,
system-frequency components, and double system-frequency components of
the first and second system models are made, wherein the unidirectional
component corresponds to transmission power or current amplitude of the
generator 12, the system-frequency component corresponds to a DC
component of the current of the generator 12, and the double
system-frequency component corresponds to negative sequence current of
the generator 12.

[0040] In detail, by electromechanical analogy, the mass-damping-spring
models of the turbine-generator and fan wheel can be analogized as an
inductance-resistance-capacitance network and then sustain a frequency
scanning by a phasor analysis, so that mode frequencies and vibration
torques in steady state are obtained. In this embodiment, a disturbance
is imposed to the generator rotor, and the frequency response of
vibration torque with the frequency of the disturbance gradually
increased from 0.01 Hz to 140 Hz is obtained, wherein an interval of 0.01
Hz between a prior frequency and a present frequency of the disturbance
is preferable. With the frequency response of vibration torque, it is
found that all the mode frequencies are out of regions from 95%-105% of
integral times of the system frequency in the second system model
simulating the combination of the four-phase power transmission system
and turbine-generator. Besides, sensitivities of rotor shafts and fan
wheels toward the disturbance of the system-frequency component are low.

[0041] In time domain, there are 11 kinds of fault situations of the
three-phase transmission module 22 while these 11 situations can be
categorized into 5 fault types. Similarly, there are 26 kinds of fault
situations of the four-phase transmission module 42 while these 26
situations can be categorized into 9 fault types. Referring to the
following Table 1, these fault types of the three-phase transmission
module 22 and four-phase transmission module 42 are shown, which is
illustrated corresponding to the power lines "A," "B" and "C" of the
three-phase transmission module 22 and power lines "a," "b," "c" and "d"
of the four-phase transmission module 42.

[0042] Referring FIGS. 4a and 4b and Table 1, in order to simulate the
above-listed situation, each of the fault situations occurs at a 0.1 time
point from a start time in midpoints "P1," "P2" of the three-phase
transmission module 22 and four-phase transmission module 42, and thus
the vibration torques of the fan wheel and the shaft of the turbines 111
are obtained.

[0043] According to operation of the circuit breaks "CB" when faults
occur, the above fault situations can be mainly classified into a
transience type and a lasting type, wherein the circuit breaks "CB" do
not operate in the transience type but operate in the lasting type. In
the following, for both of the transience type and lasting type,
stability analyses, vibration torque analyses of the turbines, and
torsional vibration analyses under an identical capacity are discussed.

[0044] 1.1 Transient Stability Analyses of the Transience Type

[0045] The transience type usually includes the three lines grounded
situation of the three-phase transmission module 22 and the four lines
grounded situation of the four-phase transmission module 42, which are
both balanced faults with each line grounded. In transient stability
analysis, with each relationship between a restoring time period of the
first or second system model and E/M vibration torque, the peat-to-peak
torques of the fan wheel of the first and second system model have
similar sensitivities, and a worst-case restoring time period can be
determined, which is about 0.19 seconds in this embodiment. On the other
hand, if both the voltage levels of the first and second system models
are 345 kV, the capacity of power transmission lines of the second system
model is 163.3% of that of the first system model, which means that the
transient stability of the second system is better than that of the first
system.

[0046] 1.2 Vibration Torque Analyses of the Transience Type

[0047] In vibration torque analysis of the turbines, the DC component of a
phase current of one of the fault lines results in disturbances of the
electromagnetic torque of the system-frequency component, wherein the
swing of current vibrations is in positive relationship to the
unidirectional component of the electromagnetic torque, and the system
models are more sensitive to the shaft vibration than to the
unidirectional component of the electromagnetic torque. Besides, since
there is no negative sequence current in balanced faults of the
transience type, the vibration torque of a frequency doubled component of
the electromagnetic torque is totally affected by the unidirectional
component of the electromagnetic torque. However, no matter how long the
restoring time period is, the vibration torque of the second system is
lower than that of the first torque; that is, the turbine-generator 1
will be affected by the fault situation in the first system much more
than in the second system.

[0048] Moreover, regarding to the torsional vibrations of the
turbine-generator of the three-phase transmission module 22 and the
four-phase transmission module 42, they are the same in a balanced fault
due to all lines grounded or broken. Besides, a balanced fault may raise
a large shaft vibration torque because shaft vibration is sensitive to
the unidirectional component; on the other hand, unbalanced faults may
raise fan wheel vibration torques higher than those raised by balanced
faults since the blades of a fan wheel is sensitive to negative sequence
current. Therefore, an average value of the shaft torque of the second
system is smaller than that of the first system, and the fan wheel
vibration of the second system is also smaller than that of the first
system.

[0049] 1.3 Torsional Vibration Analyses Under an Identical Capacity

[0050] In the worst-case restoring time period of the second system in
four lines grounded situation, the impedance of the lines and
high-leveled side of the transformers are raised although the voltage
level of the lines is lowered. According to the angular responses of the
rotors, the transient stability is kept as well as the fault current of
the midpoint "P2" is lowered, and thus the electromagnetic torque
variation of the generator and torsional vibration of the turbines are
also lowered. Referring to the following Table 2, in comparison with
those of the first system, the vibrations of the shaft and fan wheel of
the second system are additionally suppressed by 19% and 26%
respectively.

[0051] In the lasting type, two step-distance relays are previously set to
monitor the a/b phases and the c/d phases. The fault situations of the
lasting type can be simulated by the following ways: (1) single line
grounded, wherein a single phase of the circuit break "CB" is broken off
and then rapidly reconnects; (2) two opposite lines connected or
grounded, wherein two phases of the circuit break "CB" monitored by
different step-distance relays are broken off and then rapidly reconnect;
(3) two adjacent lines connected or grounded, wherein two phases of the
circuit break "CB" monitored by a single step-distance relay are broken
off without auto-reconnection; (4) three lines connected of grounded,
wherein all phases of the circuit break "CB" are broken off without
auto-reconnection.

[0052] 2.1 Transient Stability Analyses of the Lasting Type

[0053] Swing of the angular responses of the rotors of the second system
is small and transient stability is preferred since the capacity of the
second system with voltage level of 345 kV is raised by 66.7%. On the
other hand, while the first system and the second system with voltage
level of 211 kV have the same power capacity and the impedance of the
second system with voltage level of 211 kV is large, a stable rotor angle
of the second system, which is 42.5 degrees, is larger than another
stable rotor angle of the first system, which is 40.5 degrees.

[0054] 2.2 Vibration Torque Analyses of the Lasting Type

[0055] In the time period of a single phase of the circuit break "CB" from
broken off to reconnection, both of the first and second systems are in a
fault state with a single line opening, which results in an unbalanced
operation and a negative sequence current toward the generator, and thus
there is frequency doubled component in the electromagnetic torque of the
generator. Furthermore, since the second system has large line impedance,
the negative sequence current is large and may make the frequency doubled
component obvious.

[0056] In sum, with the above analysis method of the present invention,
models and analyses are made for ensuring the feasibility and
effectiveness of a four-phase power transmission system.

[0057] Although the invention has been described in detail with reference
to its presently preferable embodiment, it will be understood by one of
ordinary skill in the art that various modifications can be made without
departing from the spirit and the scope of the invention, as set forth in
the appended claims.